$L^p$-estimates on functions of the Laplace operator

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$L^p$-estimates on functions of the Laplace operator

Michael E. Taylor

Source: Duke Math. J. Volume 58, Number 3 (1989), 773-793.

First Page: Show

Primary Subjects: 58G25

Secondary Subjects: 35P05, 47F05, 58G15

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077307678
Mathematical Reviews number (MathSciNet): MR1016445
Zentralblatt MATH identifier: 0691.58043
Digital Object Identifier: doi:10.1215/S0012-7094-89-05836-5

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References

[1] J.-P. Anker and N. Lohoué, Multiplicateurs sur certains espaces symétriques, Amer. J. Math. 108 (1986), no. 6, 1303–1353.

Mathematical Reviews (MathSciNet): MR88c:43008

Zentralblatt MATH: 0616.43009

Digital Object Identifier: doi:10.2307/2374528

JSTOR: links.jstor.org

[2] I. Chavel, Eigenvalues in Riemannian Geometry, Pure and Applied Mathematics, vol. 115, Academic Press Inc., New York, 1984.

Mathematical Reviews (MathSciNet): MR86g:58140

Zentralblatt MATH: 0551.53001

[3] J. Cheeger, A lower bound for the smallest eigenvalue of the Laplacian, Problems in analysis (Papers dedicated to Salomon Bochner, 1969), Princeton Univ. Press, Princeton, N. J., 1970, pp. 195–199.

Mathematical Reviews (MathSciNet): MR53:6645

Zentralblatt MATH: 0212.44903

[4] J. Cheeger, M. Gromov, and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982), no. 1, 15–53.

Mathematical Reviews (MathSciNet): MR84b:58109

Zentralblatt MATH: 0493.53035

Project Euclid: euclid.jdg/1214436699

[5] J. L. Clerc and E. M. Stein, $L\spp$-multipliers for noncompact symmetric spaces, Proc. Nat. Acad. Sci. U.S.A. 71 (1974), 3911–3912.

Mathematical Reviews (MathSciNet): MR51:3803

Zentralblatt MATH: 0296.43004

Digital Object Identifier: doi:10.1073/pnas.71.10.3911

JSTOR: links.jstor.org

[6] M. G. Cowling, Harmonic analysis on semigroups, Ann. of Math. (2) 111 (1983), no. 2, 267–283.

Mathematical Reviews (MathSciNet): MR84h:43004

Zentralblatt MATH: 0528.42006

Digital Object Identifier: doi:10.2307/2007077

JSTOR: links.jstor.org

[7] E. B. Davies, B. Simon, and M. Taylor, $L\sp p$ spectral theory of Kleinian groups, J. Funct. Anal. 78 (1988), no. 1, 116–136.

Mathematical Reviews (MathSciNet): MR89m:58205

Zentralblatt MATH: 0644.58022

Digital Object Identifier: doi:10.1016/0022-1236(88)90135-8

[8] S. Helgason, Lie Groups and Geometric Analysis, Academic Press, New York, 1984.

Mathematical Reviews (MathSciNet): MR754767

[9] S. Helgason and K. Johnson, The bounded spherical functions on symmetric spaces, Advances in Math. 3 (1969), 586–593 (1969).

Mathematical Reviews (MathSciNet): MR40:2787

Zentralblatt MATH: 0188.45405

Digital Object Identifier: doi:10.1016/0001-8708(69)90010-3

[10] N. Lohoué, Comparaison des champs de vecteurs et des puissances du laplacien sur une variété riemannienne à courbure non positive, J. Funct. Anal. 61 (1985), no. 2, 164–201.

Mathematical Reviews (MathSciNet): MR86k:58117

Zentralblatt MATH: 0605.58051

Digital Object Identifier: doi:10.1016/0022-1236(85)90033-3

[11] N. Lohoué and Th. Rychener, Die Resolvente von $\Delta$ auf symmetrischen Räumen vom nichtkompakten Typ, Comment. Math. Helv. 57 (1982), no. 3, 445–468.

Mathematical Reviews (MathSciNet): MR84m:58163

Zentralblatt MATH: 0505.53022

Digital Object Identifier: doi:10.1007/BF02565869

[12] H. P. McKean, An upper bound to the spectrum of $\Delta$ on a manifold of negative curvature, J. Differential Geometry 4 (1970), 359–366.

Mathematical Reviews (MathSciNet): MR42:1009

Zentralblatt MATH: 0197.18003

Project Euclid: euclid.jdg/1214429509

[13] R. Schrader and M. E. Taylor, Small $\hbar$ asymptotics for quantum partition functions associated to particles in external Yang-Mills potentials, Comm. Math. Phys. 92 (1984), no. 4, 555–594.

Mathematical Reviews (MathSciNet): MR86f:81134

Zentralblatt MATH: 0534.58028

Digital Object Identifier: doi:10.1007/BF01215284

Project Euclid: euclid.cmp/1103940931

[14] R. Schrader and M. E. Taylor, Semiclassical asymptotics, gauge fields, and quantum chaos, J. Funct. Anal., to appear.

Mathematical Reviews (MathSciNet): MR995750

Zentralblatt MATH: 0679.58046

Digital Object Identifier: doi:10.1016/0022-1236(89)90021-9

[15] R. J. Stanton and P. A. Tomas, Expansions for spherical functions on noncompact symmetric spaces, Acta Math. 140 (1978), no. 3-4, 251–276.

Mathematical Reviews (MathSciNet): MR58:23365

Zentralblatt MATH: 0411.43014

Digital Object Identifier: doi:10.1007/BF02392309

[16] E. M. Stein, Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. , Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J., 1970.

Mathematical Reviews (MathSciNet): MR40:6176

Zentralblatt MATH: 0193.10502

[17] R. S. Strichartz, Analysis of the Laplacian on the complete Riemannian manifold, J. Funct. Anal. 52 (1983), no. 1, 48–79.

Mathematical Reviews (MathSciNet): MR84m:58138

Zentralblatt MATH: 0515.58037

Digital Object Identifier: doi:10.1016/0022-1236(83)90090-3

[18] M. E. Taylor, Fourier integral operators and harmonic analysis on compact manifolds, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978), Part 2, Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 115–136.

Mathematical Reviews (MathSciNet): MR81i:58042

Zentralblatt MATH: 0429.35055

[19] M. E. Taylor, Pseudodifferential operators, Princeton Mathematical Series, vol. 34, Princeton University Press, Princeton, N.J., 1981.

Mathematical Reviews (MathSciNet): MR82i:35172

Zentralblatt MATH: 0453.47026

[20] S. Y. Cheng, P. Li, and S.-T. Yau, On the upper estimate of the heat kernel of a complete Riemannian manifold, Amer. J. Math. 103 (1981), no. 5, 1021–1063.

Mathematical Reviews (MathSciNet): MR83c:58083

Zentralblatt MATH: 0484.53035

Digital Object Identifier: doi:10.2307/2374257

JSTOR: links.jstor.org

[21] M. Reed and B. Simon, Methods of modern mathematical physics. II. Fourier analysis, self-adjointness, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1975.

Mathematical Reviews (MathSciNet): MR58:12429b

Zentralblatt MATH: 0308.47002

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